IPP is based on the Graphplan approach, which means it performs iterative deepening A* search using an admissible heuristic. To compute the heuristic, Graphplan and related planners build a levelled graph structure which presents an "optimistic" view of the set of reachable states: to be precise, if a set of facts F are found at level k in the graph, it may be possible to reach a state in which all the facts in F are true in k time steps, but it is not guaranteed. If, on the other hand, all facts in F are not found at level k, it is guaranteed that there exists no plan with k or fewer time steps that achieves all the facts in F. Therefore, the planner starts by building the graph, level by level, until a level is reached in which all the goal facts can be found. Then, a backward search through the graph is made to check if the goals are actually reachable, and to find a plan if that is the case. If this fails, the graph is extended another level and the backward search tried again.
The graph constructed has the property that the set of "maybe reachable facts" is monotonically increasing with each level, so at some point, all possibly reachable facts will be included and extending the graph by another level will give nothing new. If at this point, all the goal facts are not found in the last level, the goal is provably unreachable and the planner exits.
time: 0, 51 facts and 0 exclusive pairs
57 ops and 14 exclusive pairs
time: 1, 62 facts and 15 exclusive pairs
78 ops and 129 exclusive pairs
.
.
.
time: 11, 90 facts and 144 exclusive pairs
goals first reachable in 11 time steps
From the first level where the goal facts are found, backward search
is tried at each level. Eventually, all possibly reachable facts are
in the graph (the graph "levels off"). At this point, IPP starts using
something called a "wave front", which is a more memory-efficient
representation for the graph:
156 ops and 1812 exclusive pairs
time: 12, 90 facts and 144 exclusive pairs ( 39, 141 positives)
graph has leveled off! wave front mechanism is taking over
If the problem instance is solvable, the planner eventually reaches
a level at which the backwards search succeeds and it finds a plan:
expanding wave front to level 13
found plan as follows:
time step 0: LOAD PACKET2 TRUCK3 OFFICE3
DRIVE TRUCK2 AIRPORT2 OFFICE2 CITY2
FLY AIRPLANE1 AIRPORT1 AIRPORT3
DRIVE TRUCK1 AIRPORT1 OFFICE1 CITY1
time step 1: LOAD PACKET1 TRUCK1 OFFICE1
DRIVE TRUCK3 OFFICE3 AIRPORT3 CITY3
LOAD PACKET3 TRUCK2 OFFICE2
.
.
.
Some clues about the behaviour of IPP on a particular problem can be
elucidated from the output: